Systems that derive wave fields of seismic energy within a seismic volume of interest from seismic data recorded at or near the surface of the seismic volume of interest are known. These systems implement various techniques for deriving the seismic wave fields.
For example, some of these techniques implement ray-based principles that decompose wave fields recorded at or near the surface to extrapolate the seismic waves downward into the earth as rays. Some such techniques implement summation of a set of functions, such as Gaussian beams, to describe propagation of seismic energy as beams. While the use of beams to describe the waves propagating through the seismic volume of interest enhances ray-based processing, the accuracy of these techniques is still lacking for seismic volumes containing complex structures. The accuracy of ray-based analysis is especially degraded at lower frequencies, where wave propagation becomes less localized.
As another example, some techniques for deriving subsurface wave fields use finite-element methods to describe subsurface seismic wave fields. While the accuracy of these techniques is generally superior to ray-based analysis, particularly at lower frequencies and for complex structures, finite-element techniques tend to be resource intensive. For example, finite-element techniques tend to require extensive computing resources, such as processing and/or storage, and may require a significant amount of time. Moreover, ray-based methods support the conceptualization, analysis and interpretation of seismic energy propagation much more than purely numerical methods such as standard finite element and finite difference methods.